{"paper":{"title":"On the Mellin transforms of powers of Hardy's function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2010-01-12T09:07:03Z","abstract_excerpt":"Various properties of the Mellin transform function $$ {\\cal M}_k(s) := \\int_1^\\infty Z^k(x)x^{-s}dx $$ are investigated, where $$ Z(t) := \\zeta(1/2+it){\\bigl(\\chi(1/2+it)\\bigr)}^{-1/2}, \\quad \\zeta(s) = \\chi(s)\\zeta(1-s) $$ is Hardy's function and $\\zeta(s)$ is Riemann's zeta-function. Connections with power moments of $|\\zeta(1/2+it)|$ are established, and natural boundaries of ${\\cal M}_k(s)$ are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1824","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}